%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM845+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:21:10 PM UTC 2026
% Result : Theorem 24.72s 4.49s
% Output : Proof 24.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 4 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 7 ~; 3 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn 5 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vmul(vsucc(vd411),vsucc(Vd413)) = vplus(vmul(vsucc(vd411),Vd413),vsucc(vd411)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd8) ).
fof(f8_nnf,plain,
! [Vd413] :
( vmul(vsucc(vd411),vsucc(Vd413)) = vplus(vmul(vsucc(vd411),Vd413),vsucc(vd411))
| vmul(vsucc(vd411),Vd413) != vplus(vmul(vd411,Vd413),Vd413) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [Vd413] :
( vmul(vsucc(vd411),vsucc(Vd413)) = vplus(vmul(vsucc(vd411),Vd413),vsucc(vd411))
| vmul(vsucc(vd411),Vd413) != vplus(vmul(vd411,Vd413),Vd413) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c9,plain,
( vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vsucc(vd411),X0),vsucc(vd411))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f0,conjecture,
! [Vd416] :
( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd0) ).
fof(f0_neg,negated_conjecture,
~ ! [Vd416] :
( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [Vd416] :
( vmul(vsucc(vd411),vsucc(Vd416)) != vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416))
& vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
( vmul(vsucc(vd411),vsucc(sk0)) != vplus(vmul(vd411,vsucc(sk0)),vsucc(sk0))
& vmul(vsucc(vd411),sk0) = vplus(vmul(vd411,sk0),sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c0,plain,
vmul(vsucc(vd411),sk0) = vplus(vmul(vd411,sk0),sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p101,plain,
vmul(vsucc(vd411),vsucc(sk0)) = vplus(vmul(vd411,vsucc(sk0)),vsucc(sk0)),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(c1,plain,
vmul(vsucc(vd411),vsucc(sk0)) != vplus(vmul(vd411,vsucc(sk0)),vsucc(sk0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p103,plain,
$false,
inference(resolution,[status(thm)],[p101,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM845+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/1.20 % Computer : n011.cluster.edu
% 0.09/1.20 % Model : x86_64 x86_64
% 0.09/1.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/1.20 % Memory : 8046.5625MB
% 0.09/1.20 % OS : Linux 6.8.0-71-generic
% 0.09/1.20 % CPULimit : 300
% 0.09/1.20 % WCLimit : 300
% 0.09/1.20 % DateTime : Thu Sep 24 05:33:13 UTC 2026
% 0.09/1.20 % CPUTime :
% 0.09/1.20 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.72/4.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.72/4.49 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------